Question

A local bank needs information concerning the savings account balances of its customers. A random sample of 15 accounts was checked. The mean balance was $586.75 with a standard deviation of $256.20. Find a 95%confidence interval for the true mean. Assume that the account balances are normally distributed. Round to the nearest cent.

A) Determine the confidence interval.

B) Would it be unusual to have a sample of 15 customer to have an average balance less than $400.00? Explain your reasoning based on the interval you determined in part A.

Answer 1

given data are:-

sample mean () = 586.75

sample sd (s) = 256.20

sample size (n) = 15

degrees of freedom = (n-1) = (15-1) = 14

t critical value for alpha= 0.05, df= 14 , both tailed test be:-

( using t distribution table  )

the 95 % confidence interval for population mean is :-

b).YES,  it would be unusual to have a sample of 15 customer to have an average balance less than $400.00. Because the value 400 lies outside the 95% confidence interval .

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